Question

Find the acute angle between the lines x + y = 0 and y = 0

Answer 1

The given lines are

x + y = 0 and y = 0

Here, A₁ = B₁ = 1, A₂ = 0, B₂ = 1.

Angle ‘θ’ between the lines is given by

θ = tan⁻¹\(\big|\frac{A_1B_2 − A_2B_1}{A_1A_2 + B_1B_2}\big|\)

= tan⁻¹\(\big|\frac{1 − 0}{0 + 1}\big|\)

= tan⁻¹ (1)

= 45°